B-737 CREW AT MDW ACKNOWLEDGES A CLRNC INTENDED FOR A COMPANY ACR AND TAXIES INTO POS ON THE RWY.

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WE WERE IN #1 POS FOR RWY 31C AFTER SPECIFICALLY REQUESTING THAT RWY. NO IDICATION OF OTHER ACFT HOLDING. AT THE SAME TIME ATC CLRED US INTO POS THE CAPT MADE AN ANNOUNCEMENT TO THE FA'S AND I AT FIRST THOUGHT HE WAS TALKING TO ME AND I DIDN'T SPECIFICALLY HEAR OUR CALL SIGN; BUT I DID HEAR CLRED INTO POS AND HOLD. I COULD READ BACK CALL SIGN; BUT TWR DID NOT CORRECT US. WHEN WE WERE IN POS; TWR CLRED ANOTHER ACFT FOR TAKEOFF ON RWY 31C; BUT IT WASN'T US. I CHALLENGED THE TWR AND THEY INFORMED US WE WERE NOT CLRED INTO POS. BUT TO JUST STAY WHERE WE WERE. THERE WAS ANOTHER ACFT BEHIND US AND APPARENTLY HE WAS THE ONE CLRED. AGAIN; WHEN I READ BACK CLRED INTO POS NEITHER THE TWR OR THE OTHER ACFT SPOKE UP TO CLARIFY. SUPPLEMENTAL INFO FROM ACN 510993: BRIEFLY WENT OFF TWR FREQ TO ADVISE FLT ATTENDANTS THERE WAS RAIN SHOWERS IN THE AREA AND IT MIGHT BE BUMPY ON DEP. WHEN BACK ON FREQ ADVISED WE HAD BEEN CLRED INTO POS AND HOLD. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR SAID THEY WERE IN LINE NEXT FOR TAKEOFF AND BELIEVED THE TWR HAD ISSUED INSTRUCTIONS FOR THEM TO TAXI INTO POS AND HOLD. HE SAID HE ACKNOWLEDGED THE CLRNC AND ADVISED THE CAPT. HE SAID THEY WERE SURPRISED WHEN THE TWR USED DIFFERENT COMPANY CALL SIGN IN THE TAKEOFF CLRNC. HE SAID BEING NEXT IN LINE; THE HEAVY RAIN; AND A RUSH TO DEPART LED TO THE MISTAKE.